For the quadratic x^2 + 2x + 1 = 0, how many real roots does it have?

For the quadratic x^2 + 2x + 1 = 0, how many real roots does it have?

• A. No real roots
• B. One real root
• C. All real numbers
• D. Two distinct real roots

Answer: (B)

This quadratic is a perfect square. It factors as (x + 1)^2. Setting it equal to zero gives (x + 1)^2 = 0, so x = -1 is the only solution. Because the squared factor repeats the same root, there is one real root (a double root). The discriminant would be zero, which exactly corresponds to a single real solution.

This quadratic is a perfect square. It factors as (x + 1)^2. Setting it equal to zero gives (x + 1)^2 = 0, so x = -1 is the only solution. Because the squared factor repeats the same root, there is one real root (a double root). The discriminant would be zero, which exactly corresponds to a single real solution.